Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Unsteadily Propagating Permeable Mode III Crack in Piezoelectric Materials

압전재료에서 비정상적으로 전파하는 투과형 모드 III 균열

  • Lee, Kwang-Ho (Dept. of Automotive Engineering, Kyungpook Nat'l Univ.)
  • 이광호 (경북대학교 자동차공학부)
  • Received : 2012.01.18
  • Accepted : 2012.06.26
  • Published : 2012.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

An unsteadily propagating permeable crack in piezoelectric materials (PMs) under anti-plane shear mechanical loading and in-plane electric loading is studied. The equilibrium equations for a transiently propagating crack in a PM are developed, and the solutions on the stress and displacement fields for a permeable crack though an asymptotic analysis are obtained. The influences of piezoelectric constant, dielectric permittivity, time rate of change of the crack tip speed and time rate of change of stress intensity factor on the stress and displacement fields at the transiently propagating crack tip are explicitly clarified. By using the stress and displacements, the characteristics of the stress and displacement at a transiently propagating crack tip in a PM are discussed.

면외 기계적하중과 면내 전기적하중을 받는 압전재료에서 비정상적으로 전파하는 전기투과형 균열에 대하여 연구하였다. 비정상적으로 전파하는 균열에 대한 평형방정식을 개발하였고 근접해법으로 투과형균열에 대한 응력장 및 변위장을 얻었다. 압전상수, 유전율 그리고 균열선단속도 및 응력확대계수의 시간 변화율이 비정상적으로 전파하는 균열선단부근의 응력 및 변위장에 미치는 영향을 명확히 나타내었다. 이러한 응력장과 변위장을 사용하여 비정상적으로 전파하는 균열선단의 응력장 및 변위장의 특성에 대하여 토론하였다.

Keywords

References

  1. Gabbert, Y. and Tzou, H., 2001, "Smart Structure and Structonic Systems," Proceedings of IUTAM-Symposium Magdeburg 2000. Dordrecht. Springer.
  2. Yang, W., 2006, "Mechanics and Reliability of Actuating Materials, Proceedings of IUTAM-Symposium Beijing 2004," Dordrecht. Springer.
  3. Mehta, K. and Virkar, A.V., 1990, "Fracture Mechanisms in Ferroelectric-Ferroelastic Lead Zirconate Titanate (Zr:Ti=0.54:0.46)Ceramics," J. Am. Ceram. Soc., Vol. 73, pp. 567-574. https://doi.org/10.1111/j.1151-2916.1990.tb06554.x
  4. Schneider, G.A. and Heyer, V., 1999, "Influence of the Electric Field on Vikers Indentation Crack Growth in $BaTiO_{3}$," J. Eur. Ceram. Soc., Vol. 19, pp. 1299-1306 . https://doi.org/10.1016/S0955-2219(98)00424-5
  5. Cao, H. C. and Evans, A. G., 1994, "Electric-Field- Induced Fatigue Crack Growth in Piezoelectrics," J. Am. Ceram. Soc., Vol. 77, pp. 1783-1786. https://doi.org/10.1111/j.1151-2916.1994.tb07051.x
  6. Parton, V.Z., 1976, "Fracture Mechanics of Piezoelectric Materials," Acta Astron, Vol. 3, pp. 671-683. https://doi.org/10.1016/0094-5765(76)90105-3
  7. Pak, Y. E., 1990, "Crack Extension Force in a Piezoelectric Materials," Journal of Applied Mechanics , Vol. 57, pp. 647-653. https://doi.org/10.1115/1.2897071
  8. Sosa, H. A., 1992, "On the Fracture Mechanics of Piezoelectric Solids," Int. J. Solids Struct., Vol. 29(21), 2613-2622. https://doi.org/10.1016/0020-7683(92)90225-I
  9. Suo, Z., Kuo, C. M., Barnett, D.M. and Willis, J. R., 1992, "Fracture Mechanics for Piezoelectric Cermics," J. Mech. Phys. Solids, Vol. 40, 739-765. https://doi.org/10.1016/0022-5096(92)90002-J
  10. Pak S.B. and Sun C.T., 1995, "Fracture Criteria for Piezoelectric Ceramics," J. Amer.Ceram.Soc.,Vol.78, pp. 1475-1480. https://doi.org/10.1111/j.1151-2916.1995.tb08840.x
  11. Chen, Z.T., Karihaloo, B.L. and Yu, S. W., 1998, "A Griffith Crack Moving Along the Interface of Two Dissimilar Piezoelectric Materials," Int.J. Fracture, Vol. 91, pp. 197-203. https://doi.org/10.1023/A:1007479401141
  12. Lee, K. H., 2010, "Impermeable Mode III Crack Propagation in Orthotropic Piezoelectric Materials," J. of Research Institute of Mech.Tech,Vol. 10, pp. 9-16.
  13. Lee, K. H., 2010, "Stress and Displacement Fields for a Propagating Mode III Crack in Functionally Graded Piezoelectric Materials," J. of Research Institute of Mech.Tech.,Vol.11, pp. 11-20.
  14. Lee, K. H., 2011, "A Dynamic Mode III Crack Propagation in Piezoelectric Materials," Energy and Environment Research, Vol. 8,pp. 13-23.
  15. Hou, M. A., Quan, X. Q. and Bian, W. F., 2001, "Energy Release Rate and Bifurcation Angles of Piezoelectric Materials with Antiplane Moving Crack," Int. J. Fract. , Vol. 107, pp. 297-306. https://doi.org/10.1023/A:1007678728046
  16. Soh, A.K., Liu, J.X., Lee, K.L. and Fang, D.N., 2002, "On a Moving Griffith Crack in Anisotropic Piezoelectric Solids," Arch. Appl. Mech., Vol.72, pp. 458-469. https://doi.org/10.1007/s00419-002-0227-8
  17. Piva, A., Tornabene, F. and Viola, E., 2006, " Crack Propagation in a four-Parameter Piezoelectric Medium," European Journal of Mechanics A/Solids, Vol. 25, pp. 230-249 https://doi.org/10.1016/j.euromechsol.2005.09.002
  18. Li, X. F., Fan, T. Y. and Wu, X. F., 2000, "A Moving Mode III Crack at the Interface Between Two Dissimilar Piezoelectric Materials," Int. J. Engng. Sci.,Vol.38,pp. 1219-1234. https://doi.org/10.1016/S0020-7225(99)00072-5
  19. Kwon, S. M. and Lee, K. Y., 2001, "Constant Moving Crack in a Piezoelectric Block:Anti-Plane Problem," Mechanics of Materials, Vol. 33, pp. 649-657. https://doi.org/10.1016/S0167-6636(01)00082-5
  20. Li, X. F. and Fan, T. Y., 2002, "Transient Analysis of a Piezoelectric Strip with a Permeable Crack Under Anti- Plane Impact Load," International Journal of Engineering Science , Vol. 40, pp. 131-143. https://doi.org/10.1016/S0020-7225(01)00039-8
  21. Lee, K.H., 2010, "Stress and Displacement Fields of a Propagating Mode III Crack in Orthotropic Piezoelectric Materials," Trans of KSME (A), Vol. 34(6), pp. 701-708.
  22. Liu, F. and Zhong, X. C., 2010, "Transient Response of Two Collinear Dielectric Cracks in a Piezoelectric Solid Under Inplane Impacts," Applied Mechanics and Computation, Vol. 217, pp. 3779-3791. https://doi.org/10.1016/j.amc.2010.09.036
  23. Yan, Z. and Jiang, L.Y., 2009, "Study of a Propagating Finite Crack in Functionally Graded Piezoelectric Materials Considering Dielectric Medium Effect," Int. J. Solids Struct., 46 pp. 1362-1372. https://doi.org/10.1016/j.ijsolstr.2008.11.005
  24. Chen, Z.T. and Meguid, S.A., 2000, "The Transient Response of a Piezoelectric Strip with a Vertical Crack Under Electromechanical Impact Load," Int. J. Solids Struct., Vol.37 pp. 6051-6062. https://doi.org/10.1016/S0020-7683(99)00259-0
  25. Li, X. F. and Tang, G. J., 2003, Transient Response of a Piezoelectric Ceramic Strip with an Eccentric Crack Under Electromechanical Impacts, Int. J. Solids Struct. Vol. 40, pp. 3571-3588 https://doi.org/10.1016/S0020-7683(03)00082-9
  26. Ing, Y.S. and Wang, M. J., 2004, Transient Analysis of a Mode-III Crack Propagating in a Piezoelectric Medium Int. J. Solids Struct. Vol.41, pp. 6197-6214. https://doi.org/10.1016/j.ijsolstr.2004.05.019
  27. Li, S. and Metaga, P.A., 1996, "Dynamic Crack Propagation in Piezoelectric Materials-Part I. Electrode Solution," J. Mech. Phys. Solids, Vol. 44, No. 11, pp. 1799-1830. https://doi.org/10.1016/0022-5096(96)00055-5
  28. Lee, K. H., Hawong, J. S. and Choi, S. H., 1996, "A Dynamic Stress Intensity Factors $K_{1}$, $K_{11}$ and Crack Propagation Characteristics of Orthotropic Materials," Engng. Fract. Mech, Vol. 53(1), pp. 19-140.
  29. Lee, K. H., 2000, "Stress and Displacement Fields for Propagating the Crack Along the Interface of Dissimilar Orthotropic Materials Under Dynamic Mode I and II Load," J. Appl. Mech., Vol. 67, pp. 223-228. https://doi.org/10.1115/1.321171
  30. Lee, K. H., 2004 "Characteristics of a Crack Propagating Along the Gradient in Functionally Gradient Materials," Int. J. of Solids Struct., Vol. 41, pp. 2879-2898. https://doi.org/10.1016/j.ijsolstr.2004.01.004
  31. Lee, K. H., Lee, Y. J. and Cho, S. B., 2009, "Characteristics of a Transiently Propagating Crack in Functionally Graded Materials," JMST, Vol. 23, pp. 1306-1322.
  32. Lee, K. H. and Cho, S. B., 2006, " Stress and Displacement Fields of a Propagating Mode III Crack in Orthotropic Functionally Gradient Materials with Property Graduation Along X Direction," Trans of the KSME (A), Vol. 30(3), pp. 249-259.